Functions - Day One

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FunctionsUnit One

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Review

August 31st, 2011

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Definitions

Relation: a link between two variables

Independent Variable: the variable whosevariation generates the others variation

Dependent Variable: the variable whose variationreacts to the others variation

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a Function

A relation between two variables is called functional, or afunction, when no more than one value of the dependent

variable is associated with each value of the independentvariable.

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a Function

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Only one y-coordinateis associated

with each x-coordinate


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Inverse Relation

An inverse relation, or simply inverse, is obtainedby interchanging the values of each ordered pair in

a relation between two variables.

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Function Inverse

Find the inverse of a function by switching

the x and y variables.

Example:

Function

Inverse

X 1 2 3 4 5

y 2 4 6 8 10

X 2 4 6 8 10

y 1 2 3 4 5


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4

3

2

1

-1

-2

-3

-4

-4 -3 -2 -1 1 2 3 4

Draw the inverseX Y

-1 5

0 4

1 3

2 2

3 3

4 4

X Y

5 -1

4 0

3 1

2 2

3 3

4 4

Is the inverse a function? NO


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Properties of Functions

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Give the Domain & Image?

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Give the Domain & Range?

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Variation: increasing, decreasing or constant

Increasing: when a positive variation of theindependent variable leads to a positive variation of thedependent variable. (or a negative to a negative)

Decreasing: when a positive variation of the

independent variable leads to a negative variation ofthe dependent (or a negative to a positive)

Constant: when a variation of the independent variabledoes not lead to any variation of the dependent

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List the variations

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Extrema: minimum and maximum

Minimum: the smallest value of the dependentvariable

Maximum: the largest value of the dependentvariable

Sign: positive or negative

Positive: the values of the dependentvariable are positive, above the x-

axis

Negative: the values of theMiss Connell


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State the min, max and signs

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Intercept coordinates: x-intercept (zero) and yintercept (initial value)

Zeros: the value of the independentvariable when that of the dependent is

zero.

Graphically, a zero corresponds to the x-intercept.

Initial Value: the value of the dependentvariable when that of the independentvariable is zero.

Graphically, the initial value corresponds to the y-interce t.Miss Connell


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List the Zeros & Initial Value?

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Practice Questions

Visions: Page 9 #1, 3, 6

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Answers

Page 9 #1, 3, 6

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1A1. The maximum levelof traffic is 1800 people

1A2. The minimum levelof traffic is 500 people

1B. Passenger trafficequals 1200 people at: 1h,

3, 10, and 14h 1C. Passenger traffic

exceeds 1200 over: ]1,3[ h and ]10, 14[ h.

1D1. Over the interval of[0, 2] h the function isincreasing

1D1.Over the interval of

[2, 9] the function isMiss Connell


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L (cm) W(cm)

0.25 24

0.5 12

1 6

2 3

3 2

4 1.5

5 1.2

6 1

10 0.6

15 0.4

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Functions - Day One